I feel like I'm trying to claw/grip the floor with my toes when I stand on the balls of my feet, but I just fall forward. Any tips/cues/hints on how to sit down more on my shots or when I move?
Like these: https://m.champssports.com/?uri=product&sku=AQ3325&model=267265&cm=GLOBAL SEARCH: KEYWORD SEARCH That will help. Also, it sounds like you might not be bending your knees enough, which should help with center of gravity. Just an inclination.
https://www.amazon.co.uk/toe-trainers/s?ie=UTF8&page=1&rh=i:aps,k:toe trainers Makes you use the 4 archers of the foot.